Choosing between Similar and Dissimilar Information : The Role of Strategic Complementarities

We study a class of games where players face restrictions on how much information they can obtain on a common payo§ relevant state, but have some leeway in covertly choosing the similarity (or dependence) between their information sources and the other players’ sources, before simultaneously choosing actions. Using a new stochastic dependence ordering, we show that when agents play actions that are increasing in the signal they receive, each player chooses to observe information that is more dependent on the information of other players whose actions are complements with his actions and less dependent on the information of players whose actions are substitutes with his actions. We then provide su¢cient conditions for information structures such as public or private information to arise in equilibrium. Equilibrium information structures may be ine¢cient. Making which sources were chosen (but not their realizations) publicly observable may restore e¢ciency. Information choice may also cause nontrivial equilibrium multiplicity.